diff --git a/narwhals/dataframe.py b/narwhals/dataframe.py
index a784da6a8..3e2ab225c 100644
--- a/narwhals/dataframe.py
+++ b/narwhals/dataframe.py
@@ -118,6 +118,9 @@ def select(
             self._dataframe.select(*exprs, **named_exprs),
         )
 
+    def rename(self, mapping: dict[str, str]) -> Self:
+        return self._from_dataframe(self._dataframe.rename(mapping))
+
     def filter(self, *predicates: IntoExpr | Iterable[IntoExpr]) -> Self:
         predicates, _ = self._flatten_and_extract(*predicates)
         return self._from_dataframe(
diff --git a/narwhals/pandas_like/dataframe.py b/narwhals/pandas_like/dataframe.py
index bc24d2a76..e7280bd92 100644
--- a/narwhals/pandas_like/dataframe.py
+++ b/narwhals/pandas_like/dataframe.py
@@ -121,7 +121,7 @@ def with_columns(
     ) -> Self:
         new_series = evaluate_into_exprs(self, *exprs, **named_exprs)
         df = self._dataframe.assign(
-            **{series.name: series._series for series in new_series}
+            **{series.name: validate_dataframe_comparand(series) for series in new_series}
         )
         return self._from_dataframe(df)
 
diff --git a/narwhals/pandas_like/series.py b/narwhals/pandas_like/series.py
index c9403ba90..6ef9bc63e 100644
--- a/narwhals/pandas_like/series.py
+++ b/narwhals/pandas_like/series.py
@@ -41,6 +41,9 @@ def _from_series(self, series: Any) -> Self:
             implementation=self._implementation,
         )
 
+    def __len__(self) -> int:
+        return self.shape[0]
+
     @property
     def name(self) -> str:
         return self._name
diff --git a/narwhals/pandas_like/utils.py b/narwhals/pandas_like/utils.py
index d3be72af7..038dc8162 100644
--- a/narwhals/pandas_like/utils.py
+++ b/narwhals/pandas_like/utils.py
@@ -70,7 +70,7 @@ def validate_dataframe_comparand(other: Any) -> Any:
     if isinstance(other, PandasSeries):
         if other.len() == 1:
             # broadcast
-            return item(other)
+            return item(other._series)
         return other._series
     return other
 
@@ -106,7 +106,6 @@ def parse_into_expr(implementation: str, into_expr: IntoExpr) -> PandasExpr:
         return into_expr._call(plx)  # type: ignore[no-any-return]
     if isinstance(into_expr, str):
         return plx.col(into_expr)
-    # todo: what if it's a Series?
     msg = f"Expected IntoExpr, got {type(into_expr)}"
     raise TypeError(msg)